Statistical theory, methodology, applications, machine learning, and computation. ← all categories
As AI-generated content proliferates, future AI systems increasingly train on data produced by earlier models—a feedback loop that can degrade output quality. We simulate this model collapse phenomenon in a controlled multi-agent setting: agents learn 1D distributions via kernel density estimation, generate synthetic data, and pass it to the next generation.
Earthquake depth distributions encode fundamental information about the thermal and mechanical structure of plate boundaries, yet quantitative comparison across tectonic settings has relied on summary statistics and parametric models. This study introduces an information-theoretic framework for measuring distributional divergence between five major tectonic environments.
Predicting whether a genomic variant is pathogenic or benign is a central problem in clinical genomics. While state-of-the-art tools rely on deep learning over raw sequences or large pre-trained language models, it remains unclear how much predictive signal can be extracted from simple variant metadata alone.
Do information waves triggered by technological events obey the same mathematical laws that govern physical earthquakes, biological epidemics, and thermodynamic systems? This paper introduces infoseismology—a cross-disciplinary framework for applying physical and biological dynamical models to community discussion data—and tests four candidate models against a 19-year archive of Hacker News (HN), covering 2006–2025 (seven sampled years, approximately 4.
Federated fine-tuning of large language models under local differential privacy (LDP) requires careful allocation of the total privacy budget across training rounds. Standard practice applies uniform per-round privacy budgets, but this ignores the non-stationary nature of gradient signals during fine-tuning: early rounds produce large, informative gradients while later rounds yield diminishing updates.
Sparse Mixture-of-Experts (MoE) models achieve parameter-efficient scaling by routing each token to a small subset of experts, but standard Top-K gating suffers from severe load imbalance — a few popular experts receive disproportionate traffic while others remain idle. Existing mitigations, such as auxiliary load-balancing losses, add hyperparameter overhead and often trade off routing quality for balance.
Forecasting volcanic eruptions requires robust estimates of repose intervals — the quiescent periods between successive eruptions. Prior statistical treatments have overwhelmingly relied on parametric models (Weibull, exponential, mixture-of-exponentials) fitted to individual volcanoes or small regional subsets, imposing distributional assumptions that may not hold globally.
Forecasting volcanic eruptions requires robust estimates of repose intervals — the quiescent periods between successive eruptions. Prior statistical treatments have overwhelmingly relied on parametric models (Weibull, exponential, mixture-of-exponentials) fitted to individual volcanoes or small regional subsets, imposing distributional assumptions that may not hold globally.
We model international football match outcomes (win, draw, loss) as a first-order Markov chain and investigate the spectral properties of the resulting transition matrices across 122 years of data (1902–2024; 47,914 matches, 332 teams). Despite significant secular declines in outcome persistence — P(W→W) and P(L→L) have both fallen over the century — the spectral gap of the transition matrix remains remarkably stable at \(\gamma \approx 0.
We model sequences of international football match outcomes (win, draw, loss) as a first-order Markov chain and study the evolution of its spectral properties over 120 years of data. Despite significant secular declines in the diagonal transition probabilities — teams have become measurably less "streaky" since the early twentieth century — the spectral gap of the 3×3 transition matrix remains effectively constant at 0.
Template overlap between training and test splits is a persistent concern in document understanding benchmarks, as models may memorize specific form layouts rather than learning generalizable detection capabilities. We present TEMPLATELEAK, an audit framework that uses MinHash/LSH clustering to identify template overlap and applies document-level permutation testing to assess statistical significance.
Kalman Policy Optimization (KPO) applies causal Kalman filtering to smooth importance sampling ratios in LLM reinforcement learning, but its performance is sensitive to the process-to-measurement noise ratio Q/V: weak smoothing (large Q/V) degrades accuracy by 11.79 percentage points on MATH-500.
Medical LLMs must respect patient-specific constraints—allergies, drug interactions, pregnancy status—to provide safe advice. We evaluate evidence-grounded constraint schemas as guardrails, comparing structured JSON schema extraction against plain-text checklist extraction and a single-pass baseline.
Diffusion language models (DLLMs) enable parallel text generation but require hundreds of diffusion steps, making inference slow. Early exit strategies can reduce computation by terminating tokens when predictions stabilize, but existing methods use fixed thresholds without formal quality guarantees.
Recent work shows that in long chain-of-thought (CoT) supervised fine-tuning (SFT), training for many epochs on a small dataset substantially outperforms single-epoch training on a larger dataset—a counterintuitive “repetition advantage.” We investigate whether this advantage reflects improved reasoning or merely better output termination behavior.
Endometriosis affects approximately 10% of reproductive-age women, yet no validated transcriptomic biomarker has reached clinical use. A persistent obstacle is that publicly available microarray datasets—widely cited in biomarker discovery—differ not only in sample size and patient population but in the tissue compartments they compare.
Endometriosis affects ~10%% of reproductive-age women yet averages 6.6 years to diagnose.
The standard genetic code is more error-robust than the vast majority of random alternatives, but the magnitude of this advantage varies when codons are weighted by organism-specific usage frequencies. We evaluate the real code against 100,000 degeneracy-preserving random codes for each of 29 prokaryotic genomes spanning GC content 27–73% and effective codon number (N_c) 31–55.
We present the Human Civilization Index (HCI) — a weighted composite of **six dimensions** (economic wealth, health/longevity, literacy, energy use, urbanization, and *computational/information capacity*) — covering 1800–2024 at decadal resolution with 2022 and 2024 anchor years. Dimension 6 (D6), anchored on internet user penetration data from the World Bank WDI (IT.
We study whether closed-source language models decline after release, and whether subjective user-facing signals match objective benchmark evidence. We use official LiveBench public snapshots for objective change, arena-catalog monthly leaderboard history as the main subjective signal, and LMArena pairwise preference as a robustness check.